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Chapter 27 | Wave Optics
angle of 18.4º to the direction of polarization. Verify this
beaker has a mass of 30.0 grams and contains 250 grams of
water. (b) Do the polarizing filters get hot? Explain.
89. Show that if you have three polarizing filters, with the
second at an angle of 45º to the first and the third at an
angle of
90.0º to the first, the intensity of light passed by the
first will be reduced to 25.0% of its value. (This is in contrast
to having only the first and third, which reduces the intensity
to zero, so that placing the second between them increases
the intensity of the transmitted light.)
I is the intensity of light transmitted by two
polarizing filters with axes at an angle θ and I′ is the
intensity when the axes are at an angle 90.0º−θ, then
I + I′ = I 0, the original intensity. (Hint: Use the
90. Prove that, if
trigonometric identities
cos (90.0º−θ) = sin θ and
cos θ + sin θ = 1. )
91. At what angle will light reflected from diamond be
completely polarized?
92. What is Brewster’s angle for light traveling in water that is
reflected from crown glass?
93. A scuba diver sees light reflected from the water’s
surface. At what angle will this light be completely polarized?
94. At what angle is light inside crown glass completely
polarized when reflected from water, as in a fish tank?
95. Light reflected at 55.6º from a window is completely
polarized. What is the window’s index of refraction and the
likely substance of which it is made?
96. (a) Light reflected at 62.5º from a gemstone in a ring is
completely polarized. Can the gem be a diamond? (b) At what
angle would the light be completely polarized if the gem was
in water?
97. If
θ b is Brewster’s angle for light reflected from the top of
an interface between two substances, and
θ′ b is Brewster’s
angle for light reflected from below, prove that
θ b + θ′ b = 90.0º.
98. Integrated Concepts
If a polarizing filter reduces the intensity of polarized light to
50.0% of its original value, by how much are the electric and
magnetic fields reduced?
99. Integrated Concepts
Suppose you put on two pairs of Polaroid sunglasses with
their axes at an angle of 15.0º . How much longer will it take
the light to deposit a given amount of energy in your eye
compared with a single pair of sunglasses? Assume the
lenses are clear except for their polarizing characteristics.
100. Integrated Concepts
(a) On a day when the intensity of sunlight is 1.00 kW / m 2 ,
a circular lens 0.200 m in diameter focuses light onto water in
a black beaker. Two polarizing sheets of plastic are placed in
front of the lens with their axes at an angle of 20.0º.
Assuming the sunlight is unpolarized and the polarizers are
100% efficient, what is the initial rate of heating of the water
ºC / s , assuming it is 80.0% absorbed? The aluminum